Chapter 414: Two Ways

Translator: Henyee Translations  Editor: Henyee Translations

When Professor Fefferman heard him, he was stunned.

He quickly asked in a serious tone, “Can you elaborate?”

“Of course.” Lu Zhou picked up the chalk and said, “But I need to use the blackboard.”

Once Lu Zhou had the idea, doing the calculations was just a matter of the application of mathematics.

It took about half an hour for him to fill in two blackboards.

Lu Zhou took a step back and looked at the calculations on the blackboard. He gently squeezed the chalk in his hand as he spoke confidently.

“In short, using the abstract proof method, we can only calculate the existence of T1 (>0). Therefore, the weak solution is smooth only in the time (0, T1), but the value of T1 is undetermined.”

This conclusion was wildly different from the proposed conclusion by the Millennium Prize Problem. This was probably equivalent to the difference between Newton’s law of motion and the special theory of relativity.

The former defined the specific initial value and only applied to a finite time domain. The Navier–Stokes equation was about the existence of a smooth solution under three-dimensional conditions.

The reason why the equation they constructed exploded was that they set the known value at t=T1, and therefore, it exploded when the specific time value was outside of (0, T1).

This was exactly like how Newton’s law of motion wasn’t applicable in objects with a high velocity…

When Fefferman heard Lu Zhou’s statement, he was speechless.

“… If you knew this already, why didn’t you tell me earlier?”

Lu Zhou said apologetically, “… I only thought about it just now.”

Professor Fefferman stared quietly at the blackboard for around ten minutes as he read the calculations over and over again. He then sighed.

“You are right; our previous idea wasn’t perfect.”

Things often became less mysterious once they were revealed.

Professor Fefferman paused for a second before he said, “However, as per what you said, if we can determine the T1 value is within a specific time interval of the Navier–Stokes equations, then a smooth solution exists.”

Lu Zhou was stunned. He didn’t expect Fefferman to persist with his abstract proof method.

Lu Zhou thought for a moment before he replied, “It’s not enough. We have to find a precise way to distinguish the original operator B from the constructed bilinear operator B’.”

Professor Fefferman sighed and said, “I know, but I think using our original research results is easier than using another idea. In my opinion, I think the abstract proof has potential.”

He went silent for a moment before he continued, “Since we are both people that prefer independent research, we should do the research separately.”

Although Fefferman was optimistic about Lu Zhou’s new idea, he still didn’t want to give up on his abstract proof idea.

Therefore, they would research in different directions.

This increased the chance of success.

Lu Zhou nodded, showing his agreement with Professor Fefferman’s proposal.

“This is the best choice.”

Mathematics conjectures could be solved through discussion, but discussions weren’t always necessary.

Lu Zhou returned home after his nightly run. He showered and went into his study room. He then turned on his computer and continued to edit his “L Manifold” document.

L Manifold was actually already a very impressive research result.

Just like the bilinear operator B’ that Professor Fefferman constructed, even if the smooth solution of Navier–Stokes equation couldn’t be solved, the tools they created could be published as independent research.

At least they could report it at the IMU conference.

As for the use of the tools?

It was most applicable to the Navier–Stokes equation, but it could also perform topology surgery on complex nonlinear differential structures, like manifolds. This would simplify complicated problems.

As for its possible applications in other fields, that would depend on the creativity of other researchers.

Maybe one day it could be applied in theoretical physics or engineering…

Lu Zhou stared at the computer screen as he sat quietly for a long time. In the end, he decided to submit his L Manifold thesis to Annual Mathematics.

As for the IMU conference in August…

He still planned on gifting the mathematics community with the Navier-Stokes equation solution.

Obviously, his plan consisted of a challenge.

After all, he only had a vague grasp on the Navier–Stokes equation.

Lu Zhou didn’t know if he could actually solve the problem.

Soon after Lu Zhou uploaded the thesis, the L Manifold thesis passed the academic editors’ examination and went into peer review. Meanwhile, the thesis on the Collatz conjecture was published in Annual Mathematics for the world to read.

Just as Lu Zhou expected.

The Collatz conjecture thesis caused a huge sensation in the academic world…

…

Kai University, Shiing-Shen Chern Mathematics Research Institute.

The latest issue of Annual Mathematics was laid open on the table.

Academician Zhang Yuping read the thesis in its entirety before he sighed and spoke with emotion.

“Professor Lu really is brilliant. Not only is he talented, but even his students are also talented…”

Academician Zhang knew who Qin Yue was; he was actually the one that wrote Qin Yue’s recommendation letter for Princeton.

To be honest, even though Academician Zhang encouraged Qin Yue to apply for a master’s degree under Professor Lu, he didn’t have much hope for Qin Yue.

Because back then, Professor Lu had just recently solved the Goldbach’s conjecture, and there wasn’t another mathematics professor in the world that was more “wanted” than Professor Lu.

After all, that was the Goldbach’s conjecture.

The problem that troubled Gauss, Euler, and other great mathematicians; the crown of number theory.

It even attracted attention from the Times magazine.

Standing next to Academician Zhang was the director of the Shiing-Shen Chern Mathematics Research Institute, Professor Fu Lei.

This director was slightly younger than Academician Zhang, but he was also a big name in the Chinese mathematics community.

Like Academician Zhang, who researched differential geometry, the director’s main area of research wasn’t number theory. It was group theory. However, this didn’t prevent him from understanding the academic value of Lu Zhou’s thesis.

Professor Fu went silent for a while before he asked, “This thesis… Do you really think his students wrote it?”

Academician Zhang smiled and said, “Of course! Who would be so generous to give their research results to students?”

The claim of research results was an ethics issue.

Generally, it was rare for a supervisor to not steal their students’ research results.

As for allowing the students to take credit for the research…

No normal person would do this.

Professor Fu knew this, but he couldn’t help but say, “But I don’t understand! If his students can solve it, why doesn’t he solve it himself?”

“Don’t over-think it. You can’t apply normal people logic to a genius like him.” Academician Zhang smiled and said, “Maybe he’s not interested in a simple problem like this, and therefore, he handed it to his students.”

Professor Fu didn’t believe this. It sounded too ridiculous.

Collatz conjecture wasn’t just a simple problem.

Even though there weren’t that many people who researched this conjecture, there were many people that paid attention to it.

If it were him, he would never do something like this. After all, anyone that solved a conjecture like this, they could easily become an academician as long as they met the qualification and age requirements.

Academician Zhang could tell that Professor Fu was in disbelief, and so, he merely smiled and didn’t try to explain.

Academician Zhang was correct. There were some people in the mathematics world that weren’t interested in “simple” mathematical problems.

For example, Grothendieck, Hilbert…

They were all revolutionary mathematicians.

Lu Zhou was far from being revolutionary. However, he was still young and had a long way to go…

Academician Zhang paused for a second before he smiled and said, “It’s normal to not be interested. I recently heard that Professor Lu is researching another big project. In contrast, the Collatz conjecture is nothing.”

“Something better than the Collatz conjecture?” Fu Lei frowned as he asked, “Is it chemistry? Physics-related?”

Academician Zhang laughed and said, “Not related to chemistry. Kind of related to physics but not quite.”

Fu Lei couldn’t help but ask, “What is it?”

“It’s about the existence of a smooth Navier–Stokes equation solution,” Academician Zhang said while looking out the window. His tone was full of emotion as he continued, “And that’s one of the seven Millennium Prize Problems.”

Fu Lei was totally shocked.

He stood there with his mouth agape.

“… Is he at this level yet?”

“You don’t think so?” Academician Zhang smiled and said, “Otherwise, why did the country give the first-level State Natural Science Award to a 20-year-old?”

Academician Zhang heard a rumor.

Before the Science and Technology Award Conference began, he heard that the leaders of the Ministry of Science and Technology believed that Lu Zhou shouldn’t win the first-level State Natural Science Award.

After all, Lu Zhou was decades younger than the other winners.

However, in the end, the higher-ups still decided to give Lu Zhou the first-level State Natural Science Award.

There were many rumors as to why they did so.

Among them, the most credible and widely accepted rumor was that there was a highly ranked person in academia that convinced the prize committee to take this risk.

This person convinced the prize committee with only one reason.

It was rumored that the International Mathematical Union would invite Professor Lu to do a one-hour report during the Fields Medal Award Ceremony in August. Not just that, but the Nobel Prize winner Professor Ertl would also nominate Lu Zhou for this year’s Nobel Prize in Chemistry.

At first, Academician Zhang didn’t believe that Lu Zhou could solve the Millennium Prize Problem, but Lu Zhou created so many miracles that Academician Zhang couldn’t help but believe that he could do it.

Because the name Lu Zhou was always associated with miracles.

Professor Fu thought for a moment before he muttered, “… If only this guy can work at our research institute.”

Of course, he was only kidding.

Even if Professor Lu returned to China, he would definitely work at his own research institute.

Just like the Shiing-Shen Chern Mathematics Research Institute, or like the Qiu Chengtong Mathematics Research Institute…

Academician Zhang laughed and said, “Forget about it! He’ll never come work for us. However, we can try to contact his students.”

Professor Fu said, “So what you’re saying is?”

Academician Zhang said seriously, “I will write a letter to the higher-ups and recommend Qin Yue to the Thousand Talents Initiative.

“Whether he intends to return to China or continue researching, we should start preparing now!”

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